Question

Match The exponential expression on the left with the equivalent simplified expression on the right?

Answer 1

Answer:

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$y^{2}y^{4}$           ⇒ $y^{6}$

$(2y)^{2}$               ⇒ $4y^{2}$

$(\dfrac{y}{4})^{2}$  ⇒$\dfrac{y^{2}}{16}$

$2((y)^{3})^{3}$        ⇒ $2y^{9}$

Step-by-step explanation:

We have Law of Indices as follow

1.  $x^{a}x^{b}=x^{a+b}$

2. $(xy)^{a}=x^{a}y^{a}$

3. $(\dfrac{x}{y})^{a}=\dfrac{x^{a}}{y^{a}}$

4. $((x)^{a})^{b}=x^{a\times b}$

Using above identities we get

For First

$y^{2}y^{4}=y^{2+4}=y^{4}$

Therefore $y^{2}y^{4}$   ⇒ $y^{6}$

For Second

$(2y)^{2}=2^{2}y^{2}=4y^{2}$

Therefore $(2y)^{2}$   ⇒ $4y^{2}$

For Third

$(\dfrac{y}{4})^{2}=\dfrac{y^{2}}{4^{2}}=\dfrac{y^{2}}{16}$

Therefore $(\dfrac{y}{4})^{2}$  ⇒$\dfrac{y^{2}}{16}$

For Fourth

$2((y)^{3})^{3}=2y^{3\times 3}=2y^{9}$

Therefore $2((y)^{3})^{3}$   ⇒ $2y^{9}$