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Nonamiya [84]
3 years ago
13

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

Mathematics
1 answer:
Artist 52 [7]3 years ago
3 0

Answer:

Image for the above Question is Missing hence Attached below.

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}

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