Question

The value of 51/4 x (125) 0.25 is
A. 5
B 2.5
C. 50
D. 10​

Answer 1

5
1/4
×(125)
0.25
=5
0.25
×(5
3
)
0.25


=5
0.25
×5
(3×0.25)


=5
0.25
×5
0.75


=5
(0.25+0.75)
=5
1
=

Answer 2

Answer:

Step-by-step explanation:

The Power Rule for Exponents:

The exponent must be multiplied by the power in order to raise a number with an exponent.

$(a^m)^n = a^{m*n}$

Given:

The given expression is $(5)^\frac{1}{4} * (125)^{0.25}$.

To Find:

The value of $(5)^\frac{1}{4} * (125)^{0.25}$.

Solution:

$(5)^\frac{1}{4} * (125)^{0.25}$

⇒$(5)^\frac{1}{4} * (25*5)^{0.25}$

⇒$(5)^\frac{1}{4} * (5*5*5)^{0.25}$

⇒$(5)^\frac{1}{4} * (5^3)^{0.25}$

By using the power rule of exponent,

⇒$(5)^\frac{1}{4} * (5)^{3*0.25}$

The value of $3*0.25$ is $0.75$

$\frac{1}{4}$ is also written as $0.25$.

⇒$(5)^{0.25} * (5)^{0.75}$

⇒$5^{0.25+0.75}$

⇒$5^{1.00}$

⇒$5^{1}$

⇒$5$

Therefore, the value of $(5)^\frac{1}{4} * (125)^{0.25}$is $5$.

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