2^5/2^2 =_
11 answers
To evaluate \( \frac{2^5}{2^2} \), you can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \).
Applying this property here:
\[ \frac{2^5}{2^2} = 2^{5-2} = 2^3 \]
Next, calculate \( 2^3 \):
\[ 2^3 = 2 \times 2 \times 2 = 8 \]
Thus, the final answer is
\[ \boxed{8} \]
To evaluate \( \frac{6^3}{3^4} \), we can calculate the powers separately.
First, calculate \( 6^3 \):
\[ 6^3 = 6 \times 6 \times 6 = 216 \]
Next, calculate \( 3^4 \):
\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \]
Now, we can substitute these values back in:
\[ \frac{6^3}{3^4} = \frac{216}{81} \]
Next, we can simplify \( \frac{216}{81} \). We can find the GCD (Greatest Common Divisor) of 216 and 81.
Both numbers are divisible by 27:
\[ \frac{216 \div 27}{81 \div 27} = \frac{8}{3} \]
Thus, the final answer is
\[ \boxed{\frac{8}{3}} \]
To evaluate \( \frac{10^2}{6^3} \), we can calculate the powers separately.
Calculate \( 10^2 \): \[ 10^2 = 100 \]
Calculate \( 6^3 \): \[ 6^3 = 6 \times 6 \times 6 = 216 \]
Now, we can substitute these values back in:
\[ \frac{10^2}{6^3} = \frac{100}{216} \]
Next, we simplify \( \frac{100}{216} \). Both numbers can be divided by their greatest common divisor (GCD).
The GCD of 100 and 216 is 4.
Now divide both the numerator and the denominator by 4:
\[ \frac{100 \div 4}{216 \div 4} = \frac{25}{54} \]
Thus, the final simplified answer is
\[ \boxed{\frac{25}{54}} \]
To simplify \( 3^8 \times 3^{-7} \), we can use the property of exponents that states \( a^m \times a^n = a^{m+n} \).
Applying this property:
\[ 3^8 \times 3^{-7} = 3^{8 + (-7)} = 3^{8 - 7} = 3^1 \]
Now, we calculate \( 3^1 \):
\[ 3^1 = 3 \]
Thus, the final answer is
\[ \boxed{3} \]
To simplify \( \frac{8^{-8}}{8^{-7}} \), we can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \).
Applying this property:
\[ \frac{8^{-8}}{8^{-7}} = 8^{-8 - (-7)} = 8^{-8 + 7} = 8^{-1} \]
Now, \( 8^{-1} \) can be expressed as:
\[ 8^{-1} = \frac{1}{8^1} = \frac{1}{8} \]
Thus, the final answer is
\[ \boxed{\frac{1}{8}} \]
To simplify the expression \( \frac{2^2}{11^{-1}} \), we can start by rewriting the denominator:
\[ \frac{2^2}{11^{-1}} = 2^2 \times 11^1 \]
This allows us to express the equation without negative exponents.
Now, calculate \( 2^2 \):
\[ 2^2 = 4 \]
And \( 11^1 = 11 \).
Now, substitute these values back into the expression:
\[ 2^2 \times 11^1 = 4 \times 11 = 44 \]
Thus, the final answer is
\[ \boxed{44} \]
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