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Answer :
To solve the expression [tex]\(5^4 \times 5^{-6}\)[/tex], we can use the property of exponents which states that when you multiply two powers with the same base, you can add their exponents. This property is written as:
[tex]\[ a^m \times a^n = a^{m+n} \][/tex]
In this expression, both powers have the base 5. So, we can add the exponents:
1. The first exponent is 4.
2. The second exponent is -6.
Add these exponents:
[tex]\[ 4 + (-6) = -2 \][/tex]
Now, using the combined exponent, the expression becomes:
[tex]\[ 5^{-2} \][/tex]
A negative exponent indicates a reciprocal. This means:
[tex]\[ 5^{-2} = \frac{1}{5^2} \][/tex]
Next, calculate [tex]\(5^2\)[/tex]:
[tex]\[ 5^2 = 25 \][/tex]
So:
[tex]\[ \frac{1}{5^2} = \frac{1}{25} \][/tex]
Therefore, the value of [tex]\(5^4 \times 5^{-6}\)[/tex] is [tex]\(\frac{1}{25}\)[/tex].
The correct answer is C. [tex]\(\frac{1}{25}\)[/tex].
[tex]\[ a^m \times a^n = a^{m+n} \][/tex]
In this expression, both powers have the base 5. So, we can add the exponents:
1. The first exponent is 4.
2. The second exponent is -6.
Add these exponents:
[tex]\[ 4 + (-6) = -2 \][/tex]
Now, using the combined exponent, the expression becomes:
[tex]\[ 5^{-2} \][/tex]
A negative exponent indicates a reciprocal. This means:
[tex]\[ 5^{-2} = \frac{1}{5^2} \][/tex]
Next, calculate [tex]\(5^2\)[/tex]:
[tex]\[ 5^2 = 25 \][/tex]
So:
[tex]\[ \frac{1}{5^2} = \frac{1}{25} \][/tex]
Therefore, the value of [tex]\(5^4 \times 5^{-6}\)[/tex] is [tex]\(\frac{1}{25}\)[/tex].
The correct answer is C. [tex]\(\frac{1}{25}\)[/tex].
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