easy

Exponentiation problems - easy

Problem №1

If $3^n=3^2.3^3$ , find n.

Solution:
We multiply the right side and get $3^2.3^3=3^{2+3}=3^5=3^n$ , so n=5.

Problem №2

(−2)³ = ?

Solution:
(−2)³ = (−2).(−2).(−2) = -8

Problem №3

Calculate $5.3^4-2.3^5$

Solution:
$5.3^4-2.3^5=5.3^4-2.3.3^5=5.3^4-6.3^4=-1.3^4=-3.3.3.3=-81$

Problem №4

Calculate $3^4-3^3$ .

Solution:
$3^4-3^3=3^3.3-3^3.1=3^3(3-1)=3^3.2=3.3.3.2=(3.3).(3.2)=9.6=54$

Problem №5

Calculate $5^2.2^3.3$

Solution:
$5^2.2^3.3=(5.5).(2.2.2).3=25.8.3=200.3=600$

Problem №6

Calculate $2^3.3^2$

Solution:
$2^3.3^2=2.2.2.3.3=4.2.3.3=8.3.3=24.3=72$

Problem №7

Calculate $2^8$ .

Solution:
$2^8=2^{2.4}=(2^2)^4=4^4=4.4.4.4=16.4.4=64.4=256$

Problem №8

Calculate $3^4$

Solution:
$3^4=3.3.3.3=9.3.3=27.3=81$

Problem №9

Find n, such that $8^n=2^{-3}$ .

Solution:
We have $2^{-3}=(2^3)^{-1}=8^{-1}=8^n$ , so n=-1.

Problem №10

5⁰ = ?

Solution:
5⁰ = 1

Problem №11

2⁻³ = ?

Solution:
$2^3=\frac{1}{2^3}=\frac{1}{8}$

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