Topic 7: Exponents and Square Roots
For problems 1 – 4, fully simplify each of the given expressions. Express your answers
without negative exponents.
1. (2𝑥 2 )5
2. (−3𝑥)2 (6𝑥 2 )
3.
4𝑥 −6
14𝑥 −8
−1
4. (2𝑥 ) ∙ (2𝑥)−2
5. Simplify and express your answer in standard scientific notation:
4.8 × 108
. 6 × 10−2
6. Simplify: √25𝑥 8
7. Simplify: √75𝑥 5
8. Add and subtract as indicated, and fully simplify your answer:
3√20 – 7√45
9. Multiply and simplify, if possible:
10. Rationalize the denominator:
√3 ∙ √15
2
√5
ANSWERS:
1. 32𝑥10
2. 54𝑥 4
3.
4.
2𝑥 2
7
1
2𝑥 3
5. 8 × 1010
6. 5𝑥 4
7. 5𝑥 2 √3𝑥
8. –15√5
9. 3√5
10.
2√5
5
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