Express the following in exponential form: (i) (ii) (iii) (iv) (v) (vi)

Understand the Question Exponential notation is a compact way to represent repeated multiplication of the same factor. In the expression , is the base (the number or variable being multiplied) and is the exponent or power (the number of times the base appears as a factor). When an expression contains products of different factors, we group identical factors together and write each in its respective exponential form, joined by multiplication signs. Part (i) Express in exponential form. Step 1 · Express in Exponential Form The base is and it is multiplied by itself times. Answer > (i) Part (ii) Express in exponential form. Step 1 · Express in Exponential Form The base is and it is multiplied by itself times. Answer > (ii) Part (iii) Express in exponential form. Step 1 · Express in Exponential Form The base is and it is multiplied by itself times. Answer > (iii) Part (iv) Express in exponential form. Step 1 · Express in Exponential Form Group identical bases together: is multiplied times is multiplied times Answer > (iv) Part (v) Express in exponential form. Step 1 · Express in Exponential Form Group identical bases together: is multiplied times is multiplied times Answer > (v) Part (vi) Express in exponential form. Step 1 · Express in Exponential Form Group identical bases together: is multiplied times is multiplied times is multiplied time Answer > (vi) Common Mistakes Confusing Exponentiation with Multiplication: Writing repeated multiplication as a product with the count (e.g., ) instead of power form (). Combining Unlike Bases: Adding powers across different bases, such as incorrectly writing as . Writing Power of 1: Writing instead of standard simplified form .

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Question 1

Express the following in exponential form:

(i) $6 \times 6 \times 6 \times 6$

(ii) $y \times y$

(iii) $b \times b \times b \times b$

(iv) $5 \times 5 \times 7 \times 7 \times 7$

(v) $2 \times 2 \times a \times a$

(vi) $a \times a \times a \times c \times c \times c \times c \times d$

Solution

Understand the Question

Exponential notation is a compact way to represent repeated multiplication of the same factor.
In the expression $a^n$ , $a$ is the base (the number or variable being multiplied) and $n$ is the exponent or power (the number of times the base appears as a factor).
When an expression contains products of different factors, we group identical factors together and write each in its respective exponential form, joined by multiplication signs.

(i) Express $6 \times 6 \times 6 \times 6$ in exponential form.

Step 1 · Express in Exponential Form

The base is $6$ and it is multiplied by itself $4$ times.

$6 \times 6 \times 6 \times 6 = 6^4$

Answer

(i) $6^4$

(ii) Express $y \times y$ in exponential form.

Step 1 · Express in Exponential Form

The base is $y$ and it is multiplied by itself $2$ times.

$y \times y = y^2$

Answer

(ii) $y^2$

(iii) Express $b \times b \times b \times b$ in exponential form.

Step 1 · Express in Exponential Form

The base is $b$ and it is multiplied by itself $4$ times.

$b \times b \times b \times b = b^4$

Answer

(iii) $b^4$

(iv) Express $5 \times 5 \times 7 \times 7 \times 7$ in exponential form.

Step 1 · Express in Exponential Form

Group identical bases together:

$5$ is multiplied $2$ times $\implies 5^2$
$7$ is multiplied $3$ times $\implies 7^3$

$5 \times 5 \times 7 \times 7 \times 7 = (5 \times 5) \times (7 \times 7 \times 7) = 5^2 \times 7^3$

Answer

(iv) $5^2 \times 7^3$

(v) Express $2 \times 2 \times a \times a$ in exponential form.

Step 1 · Express in Exponential Form

Group identical bases together:

$2$ is multiplied $2$ times $\implies 2^2$
$a$ is multiplied $2$ times $\implies a^2$

$2 \times 2 \times a \times a = (2 \times 2) \times (a \times a) = 2^2 \times a^2$

Answer

(v) $2^2 \times a^2$

(vi) Express $a \times a \times a \times c \times c \times c \times c \times d$ in exponential form.

Step 1 · Express in Exponential Form

Group identical bases together:

$a$ is multiplied $3$ times $\implies a^3$
$c$ is multiplied $4$ times $\implies c^4$
$d$ is multiplied $1$ time $\implies d^1 = d$

$a \times a \times a \times c \times c \times c \times c \times d = (a \times a \times a) \times (c \times c \times c \times c) \times d = a^3 \times c^4 \times d$

Answer

(vi) $a^3 \times c^4 \times d$

Common Mistakes

Confusing Exponentiation with Multiplication: Writing repeated multiplication as a product with the count (e.g., $6 \times 6 \times 6 \times 6 = 6 \times 4 = 24$ ) instead of power form ( $6^4$ ).
Combining Unlike Bases: Adding powers across different bases, such as incorrectly writing $5^2 \times 7^3$ as $(5 \times 7)^{2+3} = 35^5$ .
Writing Power of 1: Writing $d^1$ instead of standard simplified form $d$ .

Question 1

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