Question

Applying properties of Exponents in exercise,use the properties of exponents to simplify the expression.See example 1.

Answer 1

Answer: a) 15625, b) 0.2, c) 625, d) 0.008.

Step-by-step explanation:

Since we have given that

a) $(5^2)(5^3)$

As we know that

$a^m\times a^n=a^{m+n}$

So, it becomes,

$5^2\times 5^3=5^{2+3}=5^6=15625$

(b) $(5^2)(5^{-3})$

So, it becomes,

$5^2\times 5^{-3}=5^{2-3}=5^{-1}=\dfrac{1}{5}=0.2$

(c) $(5^2)^2$

As we know that

$(a^m)^n=a^{mn}$

So, it becomes,

$5^{2\times 2}=5^4=625$

(d) $5^{-3}$

$a^{-m}=\dfrac{1}{a^m}\\\\5^{-3}=\dfrac{1}{5^3}=\dfrac{1}{125}=0.008$

Hence, a) 15625, b) 0.2, c) 625, d) 0.008.