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Simplify.
[tex]\[ 256^{\frac{5}{4}} \][/tex]

Answer: [tex]\(\square\)[/tex]

Sagot :

GinnyAnsweridn
To simplify [tex]\( 256^{\frac{5}{4}} \)[/tex]:

1. Express 256 as a power of 2:
[tex]\[ 256 = 2^8 \][/tex]

2. Substitute this into the given expression:
[tex]\[ 256^{\frac{5}{4}} = (2^8)^{\frac{5}{4}} \][/tex]

3. Use the power of a power property, [tex]\( (a^m)^n = a^{m \cdot n} \)[/tex]:
[tex]\[ (2^8)^{\frac{5}{4}} = 2^{8 \cdot \frac{5}{4}} \][/tex]

4. Perform the multiplication in the exponent:
[tex]\[ 8 \cdot \frac{5}{4} = 10 \][/tex]

5. Rewrite the expression with the new exponent:
[tex]\[ 2^{10} \][/tex]

6. Evaluate the expression:
[tex]\[ 2^{10} = 1024 \][/tex]

So, the simplified form of [tex]\( 256^{\frac{5}{4}} \)[/tex] is:
[tex]\[ 256^{\frac{5}{4}} = 1024 \][/tex]
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