McGraw Hill Math Grade 8 Lesson 10.3 Answer Key More about Exponents

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 10.3 More about Exponents to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 10.3 More about Exponents

Exercises

CALCULATE

Convert to a fraction.

Question 1.
4^-3
Answer:
\(\frac{1}{64}\)
Explanation:
a^-n  =1/aⁿ = \(\frac{1}{a}\)n
4^-3  =1/4³  = \(\frac{1}{4x4x4}\) = \(\frac{1}{64}\)

Question 2.
3^-3
Answer:
\(\frac{1}{27}\)
Explanation:
a^-n  =1/aⁿ = \(\frac{1}{a}\)n
3^-3  =1/3³  = \(\frac{1}{3x3x3}\) =  \(\frac{1}{27}\)

Question 3.
6^-4
Answer:
\(\frac{1}{1296}\)
Explanation:
a^-n  =1/aⁿ = \(\frac{1}{a}\)n
6^-4  =1/6⁴  = \(\frac{1}{6x6x6x6}\) =  \(\frac{1}{1296}\)

Question 4.
5^-5
Answer:
\(\frac{1}{3125}\)
Explanation:
a^-n  =1/aⁿ = \(\frac{1}{a}\)n
5^-5  =1/5⁵  = \(\frac{1}{5x5x5x5x5}\)  = \(\frac{1}{3125}\)

Question 5.
7^-2
Answer:
\(\frac{1}{49}\)
Explanation:
a^-n  =1/aⁿ = \(\frac{1}{a}\)n
7^-2  =1/7²  = \(\frac{1}{7×7}\) = \(\frac{1}{49}\)

Question 6.
4^-1
Answer:
\(\frac{1}{4}\)
Explanation:
a^-n  =1/aⁿ = \(\frac{1}{a}\)n
4^-1  =1/4¹  = \(\frac{1}{4}\) 

Question 7.
9^-5
Answer:
\(\frac{1}{59049}\)
Explanation:
a^-n  =1/aⁿ = \(\frac{1}{a}\)n
9^-5  =1/9⁵  = \(\frac{1}{9x9x9x9x9}\) = \(\frac{1}{59049}\)

Question 8.
2^-8
Answer:
\(\frac{1}{256}\)
Explanation:
a^-n  =1/aⁿ = \(\frac{1}{a}\)n
2^-8  =1/2⁸  = \(\frac{1}{2x2x2x2x2x2x2x2}\) = \(\frac{1}{256}\)

Convert to exponential form.

Question 9.
\(\frac{1}{64}\)
Answer:
8^-2 or 2^-6
Explanation:
\(\frac{1}{a}\) = 1/aⁿ = a^-n 
\(\frac{1}{64}\) = 1/ 2⁶  =2^-6  

Question 10.
\(\frac{1}{81}\)
Answer:
9^-2
Explanation:
\(\frac{1}{a}\) = 1/aⁿ = a^-n 
\(\frac{1}{81}\) = 1/ 9²  =9^-2  

Question 11.
\(\frac{1}{9}\)
Answer:
3^-2
Explanation:
\(\frac{1}{a}\) = 1/aⁿ = a^-n 
\(\frac{1}{9}\) = 1/ 3²  =3^-2  

Question 12.
\(\frac{1}{25}\)
Answer:
5^-2
Explanation:
\(\frac{1}{a}\) = 1/aⁿ = a^-n 
\(\frac{1}{25}\) = 1/ 5²  =5^-2  

Multiply

Question 13.
4⁴ × 4^-2
Answer:
16 or 4²
Explanation:
a^m x aⁿ = a^{m + n}
4⁴ x 4^-2 = 4^{4 – 2}
= 4²
= 16

Question 14.
5⁷ × 5^-4
Answer:
125 or 5³
Explanation:
a^m x aⁿ = a^{m + n}
5⁷ x 5^-4 = 5^{7 – 4}
= 5³
= 125

Question 15.
7¹² × 7^-6
Answer:
117,649 or 7⁶
Explanation:
a^m x aⁿ = a^{m + n}
7¹² x 7^-6 = 7^{12 – 6}
= 7⁶
= 117,649

Question 16.
14²⁴ × 14^-20
Answer:
38,416 or 14⁴
Explanation:
a^m x aⁿ = a^{m + n}
14²⁴ x 14^-20 = 14 ^{24 – 20}
= 14⁴
= 38,416