Solve Nested Exponents: Calculate ((15×3)^10)^10

To solve this problem, we'll follow these steps:

• Step 1: Identify the given expression.

• Step 2: Apply the power of a power rule using exponent multiplication.

• Step 3: Confirm the result against the given choices.

Now, let's work through each step:

Step 1: Identify the Given Expression.
The given expression is $\left((15 \times 3)^{10}\right)^{10}$.

Step 2: Apply the Power of a Power Rule.
According to the exponent rule, $(a^m)^n = a^{m \times n}$, we multiply the exponents:

• The base is $15 \times 3$.

• The inner exponent is 10, and the outer exponent is 10.

• So, we apply the rule: $((15 \times 3)^{10})^{10} = (15 \times 3)^{10 \times 10}$.

• This simplifies to $(15 \times 3)^{100}$.

Step 3: Confirm the Result Against the Choices.
The expression simplifies to $(15 \times 3)^{100}$.

The correct choice from the options provided is:

$\left(15\times3\right)^{100}$