Question

Express the following in exponential form with a power of 3. Write your answers on you
answer sheet.
1. 27
2.⅛
3.64y³
4.125x³
5.27x⁶y¹²​

Answer 1

Answer:

1. 3³

2. (1/2)³

3. (4y)³

4. (5x)³

5. (3x²y⁴)³

Answer 2

1. $\boxed{27=3^{3}}$

Explanation.

Here $27=3\times 3\times 3=3^{3}$

2. $\boxed{\dfrac{1}{8}=(\dfrac{1}{2})^{3}}$

Explanation.

Here $\dfrac{1}{8}=\dfrac{1^{3}}{2^{3}}=(\dfrac{1}{2})^{3}$

3. $\boxed{64y^{3}=(4y)^{3}}$

Explanation.

Here $64y^{3}=4^{3}\times y^{3}=(4\times y)^{3}=(4y)^{3}$

4. $\boxed{125x^{3}=(5x)^{3}}$

Explanation.

Here $125x^{3}=5^{3}\times x^{3}=(5\times x)^{3}=(5x)^{3}$

5. $\boxed{27x^{6}y^{12}=(3x^{2}y^{4})^{3}}$

Explanation.

Here $27x^{6}y^{12}=3^{3}\times (x^{2})^{3}\times (y^{4})^{3}$

$=(3\times x^{2}\times y^{4})^{3}=(3x^{2}y^{4})^{3}$

Note:

• $x^{a}\times y^{a}\times ...=(xy...)^{a}$