Question

Simplify using positive exponents 1. (5^3)^5 2. 7^-2/5^-2 3. -3(5+27)^0 4. 10^-2

Answer 1

Remember, when you distribute exponents, you distribute them to the existing exponent (if there is one) AND the coefficient. Here's the math:

1. $(5^3)^5$

Distribute $(^5)$ to 5 and $(^3)$

$(5^5)^3^(^5^)$

Multiply the terms accordingly

$25^1^5$

2. $\frac{7^-^2}{5^-^2}$

Multiply the numerator and denominator by 

$\frac{7^-^2}{5^-^2}=( \frac{7}{5})^-^2$

Use the Negative Exponent Rule to rearrange the expression

$(\frac{5}{7})^2$

Square the numerator and denominator

$\frac{5^2}{7^2}$

Simplify

$\frac{25}{49}$

3. $-3(5+27)^0 = 0$

If something is multiplied to the power of 0, than it is equal to 0

4. $10^-^2$

For this, we will once again use the Negative Exponents Rule (find the reciprocal and change the negative exponent to its opposite)

$\frac{1}{10^2}$

Simplify

$\frac{1}{100}$

Answers:

1. $25^1^5$

2. $\frac{25}{49}$

3. $0$

4. $\frac{1}{100}$

Hope this helps!