Question

Applying properties of Exponents In Exercise, use the properties of exponents to simplify the expression.

Answer 1

Answer:

(a) $4^7$

(b) $7^6$

(c) $\dfrac{1}{16}$

(d) $3^{4}$

Step-by-step explanation:

We need to simplify the given expressions.

(a)

Consider the given expression is

$(4^5)(4^2)$

Using the property of exponent, we get

$=4^{5+2}$            $[\because a^ma^n=a^{m+n}]$

$=4^7$

(b)

Consider the given expression is

$(7^2)^3$

Using the property of exponent, we get

$=7^{2\times 3}$            $[\because (a^m)^n=a^{mn}]$

$=7^6$

(c)

Consider the given expression is

$2^{-4}$

Using the property of exponent, we get

$=\dfrac{1}{2^{4}}$            $[\because a^{-n}=\dfrac{1}{a^n}]$

$=\dfrac{1}{16}$

(d)

Consider the given expression is

$\dfrac{3^8}{3^4}$

Using the property of exponent, we get

$=3^{8-4}$            $[\because \dfrac{a^m}{a^n}=a^{m-n}]$

$=3^{4}$