Question

Simplify by expressing radicals as rational powers, combining powers where possible. Write the simplifed expression with no quotients. Enter your answers below. Round to two decimal places if necessary.

Answer 1

-3 (Hope this is right!)

Explanation:

To simplify the expression -6/7-3, we need to express the radicals as rational powers and combine powers where possible.

Step 1: Let's start by expressing the radicals as rational powers. In this expression, there are no radicals present, so we can skip this step.

Step 2: Next, we need to combine the powers. In this case, we only have one power, which is -3.

So the simplified expression for -6/7-3 is just -3.

Therefore, the simplified expression is -3.

Answer 2

`\Large\text{$a^{(9)/(14)}\:b^(-6)$}`

Explanation:

Given expression:

`\Large\text{$\frac{a^{-(6)/(7)}b^(-3)}{a^{-(3)/(2)}b^(3)}$}`

To simplify the given expression, we can use the Quotient Law of Exponents.

`\boxed{\begin{array}{c}\underline{\sf Quotient\;Law\;of\;Exponents}\\\\(a^m)/(a^n)=a^(m-n)\\\\\end{array}}`

The Quotient Law of Exponents states that when dividing terms with the same base, subtract the exponent in the denominator from the exponent in the numerator.

Therefore:

`\Large\text{$a^{\left(-(6)/(7)-\left(-(3)/(2)\right)\right)}\cdot b^(\left(-3-3)\right)$}`

Simplify the exponents:

`\Large\text{$a^{\left(-(6)/(7)+(3)/(2)\right)}\cdot b^(\left(-3-3)\right)$}`

`\Large\text{$a^{\left(-(12)/(14)+(21)/(14)\right)}\cdot b^(\left(-6)\right)$}`

`\Large\text{$a^{\left((9)/(14)\right)}\cdot b^(\left(-6)\right)$}`

`\Large\text{$a^{(9)/(14)}\:b^(-6)$}`

If the exponents should be decimals (rounded to two decimal places), then:

`(9)/(14)=0.642857...=0.64\;\sf (2\;d.p.)`

Therefore:

`\Large\text{$a^(0.64)\: b^(-6)$}`