15 In standard form, $$ P=6.5 imes 10^{n} $$ and $$ Q=2.4 imes 10^{n} $$. Giving your answer in standard form, find in terms of $$ n $$ (a) $$ P+Q $$, (b) $$ P imes Q $$.

Question

15 In standard form, $$ P=6.5 	imes 10^{n} $$ and $$ Q=2.4 	imes 10^{n} $$. Giving your answer in standard form, find in terms of $$ n $$ (a) $$ P+Q $$, (b) $$ P 	imes Q $$.

UpStudy AI · Accepted Answer

Let's solve the problem step by step.

### Given:
- $$ P = 6.5 \times 10^{n} $$
- $$ Q = 2.4 \times 10^{n} $$

### (a) Finding $$ P + Q $$

To add $$ P $$ and $$ Q $$, we can factor out $$ 10^n $$:

$$
P + Q = 6.5 \times 10^{n} + 2.4 \times 10^{n} = (6.5 + 2.4) \times 10^{n}
$$

Now, let's calculate $$ 6.5 + 2.4 $$:
Calculate the value by following steps:
- step0: Calculate:
  $$6.5+2.4$$
- step1: Add the numbers:
  $$8.9$$
Calculating $$ 6.5 + 2.4 $$ gives us $$ 8.9 $$.

Thus, we have:

$$
P + Q = 8.9 \times 10^{n}
$$

### (b) Finding $$ P \times Q $$

To multiply $$ P $$ and $$ Q $$, we can use the property of exponents:

$$
P \times Q = (6.5 \times 10^{n}) \times (2.4 \times 10^{n}) = (6.5 \times 2.4) \times (10^{n} \times 10^{n}) = (6.5 \times 2.4) \times 10^{2n}
$$

Now, let's calculate $$ 6.5 \times 2.4 $$:
Calculate the value by following steps:
- step0: Calculate:
  $$6.5\times 2.4$$
- step1: Multiply the numbers:
  $$15.6$$
Calculating $$ 6.5 \times 2.4 $$ gives us $$ 15.6 $$.

Thus, we have:

$$
P \times Q = 15.6 \times 10^{2n}
$$

### Final Answers:
(a) $$ P + Q = 8.9 \times 10^{n} $$

(b) $$ P \times Q = 15.6 \times 10^{2n} $$
(a) $$ P + Q = 8.9 \times 10^{n} $$ (b) $$ P \times Q = 15.6 \times 10^{2n} $$

15 In standard form, and .
Giving your answer in standard form, find in terms of
(a) ,
(b) .

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15 In standard form, and . Giving your answer in standard form, find in terms of (a) , (b) .