Solve (2y ^ 5 * 2 ^ 5) * (y ^ 5 * 2 ^ 5) ^ 2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(2y^{5}2^{5})(y^{5}2^{5})^{2}$$

Evaluate

$65536y^{15}$

Solution Steps

To multiply powers of the same base, add their exponents. Add $1$ and $5$ to get $6$.

$$2^{6}y^{5}\left(y^{5}\times 2^{5}\right)^{2}$$

Calculate $2$ to the power of $6$ and get $64$.

$$64y^{5}\left(y^{5}\times 2^{5}\right)^{2}$$

Calculate $2$ to the power of $5$ and get $32$.

$$64y^{5}\left(y^{5}\times 32\right)^{2}$$

Expand $\left(y^{5}\times 32\right)^{2}$.

$$64y^{5}\left(y^{5}\right)^{2}\times 32^{2}$$

To raise a power to another power, multiply the exponents. Multiply $5$ and $2$ to get $10$.

$$64y^{5}y^{10}\times 32^{2}$$

Calculate $32$ to the power of $2$ and get $1024$.

$$64y^{5}y^{10}\times 1024$$

To multiply powers of the same base, add their exponents. Add $5$ and $10$ to get $15$.

$$64y^{15}\times 1024$$

Multiply $64$ and $1024$ to get $65536$.

$$65536y^{15}$$

Expand

$65536y^{15}$

Solution Steps

To multiply powers of the same base, add their exponents. Add $1$ and $5$ to get $6$.

$$2^{6}y^{5}\left(y^{5}\times 2^{5}\right)^{2}$$

Calculate $2$ to the power of $6$ and get $64$.

$$64y^{5}\left(y^{5}\times 2^{5}\right)^{2}$$

Calculate $2$ to the power of $5$ and get $32$.

$$64y^{5}\left(y^{5}\times 32\right)^{2}$$

Expand $\left(y^{5}\times 32\right)^{2}$.

$$64y^{5}\left(y^{5}\right)^{2}\times 32^{2}$$

To raise a power to another power, multiply the exponents. Multiply $5$ and $2$ to get $10$.

$$64y^{5}y^{10}\times 32^{2}$$

Calculate $32$ to the power of $2$ and get $1024$.

$$64y^{5}y^{10}\times 1024$$

To multiply powers of the same base, add their exponents. Add $5$ and $10$ to get $15$.

$$64y^{15}\times 1024$$

Multiply $64$ and $1024$ to get $65536$.

$$65536y^{15}$$