Studdy AI Logo
Math

QuestionSimplify −5625x83-5 \sqrt[3]{625 x^{8}} fully and express the answer in radical form.

Studdy Solution

STEP 1

Assumptions1. We are given the expression −5625x83-5 \sqrt[3]{625 x^{8}}. . We need to simplify this expression and write the answer in radical form.

STEP 2

First, we can rewrite the expression by separating the number and the variable inside the cube root.
−5625x8=−5625x8-5 \sqrt[]{625 x^{8}} = -5 \sqrt[]{625} \sqrt[]{x^{8}}

STEP 3

Next, we simplify the cube root of625. The cube root of a number is the value that, when cubed, gives the original number. The cube root of625 is5 because 53=1255^3 =125.
−56253x83=−5⋅5x83-5 \sqrt[3]{625} \sqrt[3]{x^{8}} = -5 \cdot5 \sqrt[3]{x^{8}}

STEP 4

Multiply the two constants outside the cube root.
−⋅x83=−25x83- \cdot \sqrt[3]{x^{8}} = -25 \sqrt[3]{x^{8}}

STEP 5

Now, we simplify the cube root of x8x^{8}. We know that the cube root of x3x^{3} is xx. Therefore, we can rewrite x8x^{8} as x3⋅x3⋅x2x^{3} \cdot x^{3} \cdot x^{2}.
−25x83=−25x3⋅x3⋅x23-25 \sqrt[3]{x^{8}} = -25 \sqrt[3]{x^{3} \cdot x^{3} \cdot x^{2}}

STEP 6

We can now simplify the cube root of x3⋅x3⋅x2x^{3} \cdot x^{3} \cdot x^{2}.
−25x3⋅x3⋅x23=−25⋅x⋅x⋅x23-25 \sqrt[3]{x^{3} \cdot x^{3} \cdot x^{2}} = -25 \cdot x \cdot x \cdot \sqrt[3]{x^{2}}

STEP 7

Multiply the two xx's outside the cube root.
−25⋅x⋅x⋅x23=−25x2x23-25 \cdot x \cdot x \cdot \sqrt[3]{x^{2}} = -25 x^{2} \sqrt[3]{x^{2}}So, the simplified form of −5625x3-5 \sqrt[3]{625 x^{}} is −25x2x23-25 x^{2} \sqrt[3]{x^{2}}.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord