Question

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

Answer 1

Answer:

(a) $5^{8}$

(b) 3

(c) 27

(d) $\dfrac{1}{6}$  

Step-by-step explanation:

We need simplify the given expressions.

(a)

Consider the given expression is

$(5^4)(25^2)$

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

Using the properties of exponents we get

$(5^4)(5^4)$           $[\because (a^m)^n=a^{mn}]$

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

$5^{8}$

(b)

Consider the given expression is

$(9^{\frac{1}{3}})(3^{\frac{1}{3}})$

$((3^2)^{\frac{1}{3}})(3^{\frac{1}{3}})$

Using the properties of exponents we get

$(3^{\frac{2}{3}})(3^{\frac{1}{3}})$           $[\because (a^m)^n=a^{mn}]$

$3^{\frac{2}{3}+\frac{1}{3}}$                 $[\because a^ma^n=a^{m+n}]$

$3^{1}$

$3$

(c)

Consider the given expression is

$(\dfrac{1}{3})^{-3}$

Using the properties of exponents we get

$(\dfrac{3}{1})^{3}$         $[\because a^{-n}=\dfrac{1}{a^n}]$

$3^{3}$

$27$

(d)

Consider the given expression is

$(6^4)(6^{-5})$

Using the properties of exponents we get

$6^{4+(-5)}$                  $[\because a^ma^n=a^{m+n}]$

$6^{-1}$

$\dfrac{1}{6^{1}}$         $[\because a^{-n}=\dfrac{1}{a^n}]$

$\dfrac{1}{6}$