How do you simplify this expression: (a^8a^6)^(1/7)/a^2?

Dec 14, 2016

1

Explanation:

Step 1) Combine the terms within the parenthesis using the rule for exponents:

$\textcolor{red}{{x}^{a} {x}^{b} = {x}^{a + b}}$

$\frac{{\left({a}^{8 + 6}\right)}^{\frac{1}{7}}}{a} ^ 2$

$\frac{{\left({a}^{14}\right)}^{\frac{1}{7}}}{a} ^ 2$

Step 2) Simplify the numerator by using the rule for exponents:

$\textcolor{red}{{\left({x}^{a}\right)}^{b} = {x}^{a \cdot b}}$

$\frac{{a}^{14 \cdot \frac{1}{7}}}{a} ^ 2$

${a}^{2} / {a}^{2}$

Step 3)

We can use the rule from math: $\textcolor{red}{\frac{x}{x} = 1}$

${a}^{2} / {a}^{2} = 1$

Or, we can use the rule for exponents:

$\textcolor{red}{{x}^{a} / {a}^{b} = {x}^{a - b}}$

${a}^{2} / {a}^{2} = {a}^{2 - 2} = {a}^{0} = 1$

Dec 14, 2016

Explanation:

Here are some rules when working with exponents:

$1.$ $\text{ } {x}^{m} \times {x}^{n} = {x}^{m + n}$
$2.$ $\text{ } {x}^{m} \div {x}^{n} = {x}^{m - n}$
$3.$ $\text{ } {\left({x}^{m}\right)}^{n} = {x}^{m n}$
$4.$ $\text{ } {x}^{0} = 1$

Now, to solve this question, it can be written as:

$\text{ } {\left({a}^{8} \times {a}^{6}\right)}^{\frac{1}{7}} \div {a}^{2}$
$\implies {\left({a}^{8 + 6}\right)}^{\frac{1}{7}} \div {a}^{2}$
$\implies {a}^{14 \times \frac{1}{7}} \div {a}^{2}$
$\implies {a}^{2} \div {a}^{2} = {a}^{2 - 2} = {a}^{0} = 1$