Question

simplify. express your answer using positive exponents.
$8f^{0}g^{-6}h^{-8} \cdot 9f^{0}g^{5}h^{0} \cdot 9fg^{7}h^{-1}$

Explanation:

Step1: Simplify zero exponents

Any term to the power of 0 is 1: $r^0=1$, $h^0=1$
Expression: $8 \cdot 1 \cdot g^{-6}h^{-8} \cdot 9 \cdot 1 \cdot g^5 \cdot 1 \cdot 9fg^7h^{-1} = 8g^{-6}h^{-8} \cdot 9g^5 \cdot 9fg^7h^{-1}$

Step2: Multiply constant coefficients

Multiply 8, 9, and 9 together
Expression: $8 \times 9 \times 9 = 648$

Step3: Combine $r/f$ terms

Add exponents of $f$: $f^0 \cdot f^0 \cdot f^1 = f^{0+0+1}=f^1=f$
Expression: $648f$

Step4: Combine $g$ terms

Add exponents of $g$: $g^{-6} \cdot g^5 \cdot g^7 = g^{-6+5+7}=g^6$
Expression: $648fg^6$

Step5: Combine $h$ terms

Add exponents of $h$: $h^{-8} \cdot h^0 \cdot h^{-1} = h^{-8+0-1}=h^{-9}$
Expression: $648fg^6h^{-9}$

Step6: Convert to positive exponents

Rewrite negative exponent as reciprocal: $h^{-9}=\frac{1}{h^9}$
Expression: $648fg^6 \cdot \frac{1}{h^9}$

Answer:

$\frac{648fg^6}{h^9}$