Question

(5²) ^3 × (5)^-2 ÷ (1/5)^-3​

Answer 1

Answer:

Step-by-step explanation:

In $(5^{2})^{3}$ × $5^{-2}$ ÷ $\frac{1}{5}^{-3}$ , we can simplify them step by step.

Step 1 : let’s first find the value of $(5^{2})^{3}$.

According to laws of exponents, $(a^{b})^{c} = a^{bc}$.

So, $(5^{2})^{3} = 5^{2 *3} = 5^{6}$

Step 2 : let’s find the value of $5^{-2}$.

According to laws of exponents, $a^{-b} = \frac{1}{a^{b} }$.

So, $5^{-2} = \frac{1}{5^{2} }$.

Step 3 : let’s find the value of $\frac{1}{5} ^{-3}$.

According to laws of exponents, $(\frac{x}{y})^{-b} = (\frac{y}{x} )^{b}$.

So, $(\frac{1}{5}) ^{-3} =( \frac{5}{1} )^{3} = 5^{3}$

Step 4 : this the last and important step. In this step we must bring all the simplified terms and complete the equation.

$(5^{2})^{3}$ × $5^{-2}$ ÷ $\frac{1}{5}^{-3}$ = $5^{6}$ × $\frac{1}{5^{2} }$ ÷ $5^{3}$

= $5^{2}$ ÷ $5^{3}$ × $\frac{1}{5^{2} }$

According to laws of exponents, $x^{a}$ ÷ $x^{b} = x^{a-b}$.

So, = $5^{3}$ × $\frac{1}{5^{2} }$

= ( we can cancel $5^{3}$ and $\frac{1}{5^{2} }$

= $\frac{1}{1}$ = 1

So the final answer is 1.

Hope it’s useful friend…

Good luck and have a great day….

Answer 2

Answer:

78125

Step-by-step explanation:

25^3*25÷1/5^3=.

15625*25÷1/5^3=

390625÷1/5^3 =

78125÷1^3=

=78125 this is correct answer. so the final answer is 1