Question
Simplify. Express your answer using positive exponents. \[ g^{-1} \cdot 10 g^{-1} \cdot 10 g^{0} \] Submit
Ask by Lyons Cox. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \(\frac{100}{g^{2}}\).
Solution
Calculate or simplify the expression \( g^{-1} \cdot 10g^{-1} \cdot 10g^{0} \).
Simplify the expression by following steps:
- step0: Solution:
\(g^{-1}\times 10g^{-1}\times 10g^{0}\)
- step1: Evaluate the power:
\(g^{-1}\times 10g^{-1}\times 10\times 1\)
- step2: Rewrite the expression:
\(g^{-1}\times 10g^{-1}\times 10\)
- step3: Multiply the terms:
\(g^{-1-1}\times 10\times 10\)
- step4: Subtract the numbers:
\(g^{-2}\times 10\times 10\)
- step5: Multiply the terms:
\(g^{-2}\times 100\)
- step6: Reorder the terms:
\(100g^{-2}\)
- step7: Simplify:
\(\frac{100}{g^{2}}\)
The simplified expression is \(\frac{100}{g^{2}}\).
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Simplify this solution Mind Expander
To simplify the expression \( g^{-1} \cdot 10 g^{-1} \cdot 10 g^{0} \), we start by multiplying the coefficients and combining the exponents of \( g \). First, the coefficients: \[ 10 \cdot 10 = 100. \] Next, we combine the exponents of \( g \): \[ g^{-1} \cdot g^{-1} \cdot g^{0} = g^{-1 + (-1) + 0} = g^{-2}. \] Putting it all together, we have: \[ 100 g^{-2}. \] To express this with positive exponents, we rewrite \( g^{-2} \) as \( \frac{1}{g^2} \): \[ 100 g^{-2} = \frac{100}{g^2}. \] Thus, the final simplified expression is: \[ \boxed{\frac{100}{g^2}}. \]
