Jawaban:

aⁿ × aᵐ = aⁿ⁺ᵐ

aⁿ ÷ aᵐ = aⁿ⁻ᵐ

(aⁿ)ᵐ = aⁿᵐ

(ab)ⁿ = aⁿ.bⁿ

(\frac{a}{b})^{n} = \frac{a^{n}}{b^{n}}(

b

a

)

n

=

b

n

a

n

a^{-n} = \frac{1}{a^{n}}a

−n

=

a

n

1

(\frac{a}{b})^{-n} = (\frac{b}{a})^{n}(

b

a

)

−n

=(

a

b

)

n

a⁰ = 1

Jika a^{f(x)} = a^{g(x)}a

f(x)

=a

g(x)

maka f(x) = g(x)

Pembahasan

\frac{1}{64} \: \times \: 4^{x} \: \times \: 2^{x}

64

1

×4

x

×2

x

= 64

\frac{1}{2^{6}} \: \times \: (2^{2})^{x} \: \times \: 2^{x}

2

6

1

×(2

2

)

x

×2

x

= 2⁶

2^{-6} \: \times \: 2^{2x} \: \times \: 2^{x}2

−6

×2

2x

×2

x

= 2⁶

2^{-6 + 2x + x}2

−6+2x+x

= 2⁶

2^{-6 + 3x}2

−6+3x

= 2⁶

–6 + 3x = 6

3x = 6 + 6

3x = 12

x = \frac{12}{3}

3

12

x = 4

Jadi nilai x yang memenuhi adalah x = 4