Answered

Use the properties of exponents to simplify the expression: 2532
25
3
2


Question 11 options:

A)

125

B)

25

C)

625

D)

5
Question 12 (5 points)
Solve the inequality: (x −3)12+ 2 ≥4
(
x

-
3
)
+

2

≥
4
Question 12 options:

A)

x ≥ 35

B)

x ≥ 11

C)

x ≥ 7


D)

x ≥ 13

Answer :

MRROYALGO

Question

Use the properties of exponents to simplify the expression: [tex]25^{\frac{3}{2}}[/tex]

Answer:

[tex]25^{\frac{3}{2}} = 125[/tex]\

Step-by-step explanation:

Given

[tex]25^{\frac{3}{2}}[/tex]

Required

Simplify

[tex]25^{\frac{3}{2}}[/tex]

Apply the following law of indices

[tex]a^{\frac{m}{n}} = (a^m)^{\frac{1}{n}}[/tex]

So, the expression becomes

[tex]25^{\frac{3}{2}} = (25^3)^{\frac{1}{2}}[/tex]

Express [tex]25^3[/tex] as 15625

[tex]25^{\frac{3}{2}} = (15625)^{\frac{1}{2}}[/tex]

In indices: [tex]a^{\frac{1}{2}} = \sqrt a[/tex]

So, we have:

[tex]25^{\frac{3}{2}} = \sqrt{15625[/tex]

[tex]25^{\frac{3}{2}} = 125[/tex]

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